U.S. patent application number 14/055846 was filed with the patent office on 2014-06-26 for method for generating quantized anomalous hall effect.
This patent application is currently assigned to Institute of Physics, Chinese Academy of Sciences. The applicant listed for this patent is Institute of Physics, Chinese Academy of Sciences, Tsinghua University. Invention is credited to CUI-ZU CHANG, XI CHEN, XIAO FENG, KE HE, LI LV, XU-CUN MA, LI-LI WANG, YA-YU WANG, QI-KUN XUE.
Application Number | 20140179026 14/055846 |
Document ID | / |
Family ID | 47929139 |
Filed Date | 2014-06-26 |
United States Patent
Application |
20140179026 |
Kind Code |
A1 |
XUE; QI-KUN ; et
al. |
June 26, 2014 |
METHOD FOR GENERATING QUANTIZED ANOMALOUS HALL EFFECT
Abstract
A method for generating quantum anomalous Hall effect is
provided. A topological insulator quantum well film in 3QL to 5QL
is formed on an insulating substrate. The topological insulator
quantum well film is doped with a first element and a second
element to form the magnetically doped topological insulator
quantum well film. The doping of the first element and the second
element respectively introduce hole type charge carriers and
electron type charge carriers in the magnetically doped topological
insulator quantum well film, to decrease the carrier density of the
magnetically doped topological insulator quantum well film to be
smaller than or equal to 1.times.10.sup.13cm.sup.-2. One of the
first element and the second element magnetically dopes the
topological insulator quantum well film. An electric field is
applied to the magnetically doped topological insulator quantum
well film to decrease the carrier density.
Inventors: |
XUE; QI-KUN; (Beijing,
CN) ; HE; KE; (Beijing, CN) ; MA; XU-CUN;
(Beijing, CN) ; CHEN; XI; (Beijing, CN) ;
WANG; LI-LI; (Beijing, CN) ; WANG; YA-YU;
(Beijing, CN) ; LV; LI; (Beijing, CN) ;
CHANG; CUI-ZU; (Beijing, CN) ; FENG; XIAO;
(Beijing, CN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Institute of Physics, Chinese Academy of Sciences
Tsinghua University |
Beijing
Beijing |
|
CN
CN |
|
|
Assignee: |
Institute of Physics, Chinese
Academy of Sciences
Beijing
CN
Tsinghua University
Beijing
CN
|
Family ID: |
47929139 |
Appl. No.: |
14/055846 |
Filed: |
October 16, 2013 |
Current U.S.
Class: |
438/3 |
Current CPC
Class: |
H01L 43/065 20130101;
H01L 43/14 20130101 |
Class at
Publication: |
438/3 |
International
Class: |
H01L 43/14 20060101
H01L043/14; H01L 43/06 20060101 H01L043/06 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 21, 2012 |
CN |
2012105595226 |
Claims
1. A method for generating quantum anomalous Hall effect,
comprising: forming a topological insulator quantum well film in a
range of 3QL thickness to 5QL thickness on an insulating substrate;
doping the topological insulator quantum well film with a first
element and a second element during the forming of the topological
insulator quantum well film to form a magnetically doped
topological insulator quantum well film, the doping of the
topological insulator quantum well film with the first element and
the second element respectively introducing hole type charge
carriers and electron type charge carriers in the magnetically
doped topological insulator quantum well film, to decrease the
carrier density of the magnetically doped topological insulator
quantum well film to be smaller than or equal to 1.times.10.sup.13
cm.sup.-2, one of the first element and the second element is a
magnetically dopant to the topological insulator quantum well film;
and applying an electric field to the magnetically doped
topological insulator quantum well film.
2. The method of claim 1, wherein when the insulating substrate has
a dielectric constant larger than 5000 at a temperature equal to or
smaller than 10 Kelvin, and the electric field is applied only by a
back gate structure.
3. The method of claim 1, wherein a material of the insulating
substrate is strontium titanate.
4. The method of claim 1, wherein a material of the magnetically
doped topological insulator quantum well film is represented by a
chemical formula of Cr.sub.y(Bi.sub.xSb.sub.1-x).sub.2-yTe.sub.3,
wherein 0<x<1, 0<y<2, and values of x and y satisfies
that an amount of hole type charge carriers introduced by a doping
of Cr is substantially equal to an amount of electron type charge
carriers introduced by a doping of Bi.
5. The method of claim 4, wherein 0.05<x<0.3, 0<y<0.3,
and 1:2<x:y<2:1.
6. The method of claim 5, wherein 2:3.ltoreq.x:y.ltoreq.25:22.
7. The method of claim 1, wherein the magnetically doped
topological insulator quantum well film is in 5 QL.
8. The method of claim 1, wherein when the quantum anomalous Hall
effect is achieved, an anomalous quantum resistance of the
magnetically doped topological insulator quantum well film is 25.8
k.OMEGA..
9. The method of claim 1, wherein the electric field is applied by
a liquid top gate structure located on a surface of the
magnetically doped topological insulator quantum well film.
10. The method of claim 1, wherein the electric field is applied by
a back gate structure.
Description
RELATED APPLICATIONS
[0001] This application claims all benefits accruing under 35
U.S.C. .sctn.119 from China Patent Application No. 201210559522.6,
filed on Dec. 21, 2012 in the China Intellectual Property Office,
the disclosure of which is incorporated herein by reference. This
application is related to commonly-assigned applications entitled,
"TOPOLOGICAL INSULATOR STRUCTURE," filed ______ (Atty. Docket No.
US50946); "ELECTRICAL DEVICE," filed ______ (Atty. Docket No.
US50947); "METHOD FOR MAKING TOPOLOGICAL INSULATOR STRUCTURE,"
filed ______ (Atty. Docket No. US50948); and "TOPOLOGICAL INSULATOR
STRUCTURE," filed ______ (Atty. Docket No. US50949).
BACKGROUND
[0002] 1. Technical Field
[0003] The present disclosure relates to a method for generating
quantum anomalous Hall effect.
[0004] 2. Discussion of Related Art
[0005] If an electric current flows through an electrical conductor
in a magnetic field perpendicular to the electric current, a
measurable voltage difference between two sides of the electrical
conductor, transverses to the electric current and the magnetic
field, will be produced. The presence of this measurable voltage
difference is called the Hall effect (HE) discovered by E. H. Hall
in 1879. Subsequently, the anomalous Hall effect (AHE) in magnetic
materials and the spin Hall effect (SHE) in semiconductors were
discovered. Theoretically, HE, AHE, and SHE would have
corresponding quantized forms. In 1980, K. V. Klitzing et al.
achieved quantum Hall effect (QHE) in a semiconductor in a strong
magnetic field at a low temperature (Klitzing K. V. et al., New
Method for High-Accuracy Determination of the Fine-Structure
Constant Based on Quantized Hall Resistance, Phys Rev Lett, 1980,
45:494-497). After that, D. C. Tsui et al. achieved fractional
quantum Hall effect (FQHE) during the studying of the HE in a
stronger magnetic field (Tsui D. C. et al., Two-Dimensional
Magnetotransport in the Extreme Quantum Limit. Phys Rev Lett, 1982,
48:1559-1562). In 2006, Shoucheng Zhang predicted that quantum spin
Hall effect (QSHE) can be realized in mercury telluride-cadmium
telluride semiconductor quantum wells (Bernevig B. A. et al.,
Quantum spin Hall effect and topological phase transition in HgTe
quantum wells, Science, 2006, 314:1757-1761). This prediction was
confirmed in 2007 (Konig M. et al. Qauntum spin Hall insulator
state in HgTe quantum wells. Science, 2007, 318:766-770). At
present, in the variety of quantized forms of the HE, only the
quantum anomalous Hall effect (QAHE) has not been observed in
reality. QAHE is the QHE in zero magnetic field without Landau
levels, which can have a Hall resistance of h/e.sup.2 (i.e., 25.8
k.OMEGA., i.e., quantum resistance), wherein e is the charge of an
electron and h is Planck's constant. The realizing of the QAHE can
get rid of the requirement for the external magnetic field and the
high electron mobility of the sample, and has an application
potential in real devices.
[0006] Topological insulators (TIs) are a class of new concept
quantum materials. A TI has its bulk band gapped at Fermi level,
the same as usual insulators, but hosts gapless, Dirac-type, and
spin-split surface states at all of its surfaces, which allow the
surfaces to be electrically conductive and are protected by time
reversal symmetry (TRS). There are two kinds of TIs,
three-dimensional (3D) TIs and two-dimensional (2D) TIs. 3D TIs
have topologically-protected two dimensional surface states. 2D TIs
have topologically-protected one dimensional edge states. The
discovery of Bi.sub.2Se.sub.3 group (including Bi.sub.2Se.sub.3,
Bi.sub.2Te.sub.3, and Sb.sub.2Te.sub.3) of TIs makes this kind of
material receives substantial research interest from not only
condensed matter physics but also material science. In 2010, Yu R.
et al. predicted that QAHE could be achieved in Cr or Fe doped
Bi.sub.2Se.sub.3, Bi.sub.2Te.sub.3, and Sb.sub.2Te.sub.3 3D TI
films (Yu R. et al., Quantized anomalous Hall effect in magnetic
topological insulators, Science, 2010, 329:61-64). However, any TI
which can observe the QAHE therein has not been achieved. Further,
even a ferromagnetic material (including magnetic doped TIs) having
an anomalous Hall resistance larger than a kiloohm (k.OMEGA.) has
not been achieved. For a film having a thickness of 5 nanometers
and having the anomalous Hall resistance larger than a kiloohm, the
corresponding anomalous Hall resistivity should be larger than or
equal to 0.5 milliohms.cndot.millimeter (m.OMEGA..cndot.mm).
[0007] What is needed, therefore, is to provide a method for
generating quantum anomalous Hall effect.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] Many aspects of the embodiments can be better understood
with references to the following drawings. The components in the
drawings are not necessarily drawn to scale, the emphasis instead
being placed upon clearly illustrating the principles of the
embodiments. Moreover, in the drawings, like reference numerals
designate corresponding parts throughout the several views.
[0009] FIG. 1 is a schematic view of a schematic crystal structure
of Sb.sub.2Te.sub.3, wherein (a) is a perspective view, (b) is a
top view, and (c) is a side view of 1QL.
[0010] FIG. 2 is a schematic view of an MBE reactor chamber.
[0011] FIG. 3 is a scanning tunneling microscope (STM) image of Cr
doped Sb.sub.2Te.sub.3.
[0012] FIG. 4 is a side view of one embodiment of an electrical
device.
[0013] FIG. 5 is a top view of one embodiment of the electrical
device of FIG. 4.
[0014] FIG. 6 is a graph showing magnetic field (.mu..sub.0H)
dependent Hall resistances (R.sub.yx) of one embodiment of
magnetically doped TI quantum well film at different back gate
voltages (V.sub.b), wherein a unit of R.sub.yx is quantum
resistance h/e.sup.2, which is 25.8 k.OMEGA..
[0015] FIG. 7 is a graph showing magnetic field (.mu..sub.0H)
dependent longitudinal resistances (R.sub.xx) of the embodiment of
FIG. 6 at different back gate voltages (V.sub.b), wherein a unit of
R.sub.xx is quantum resistance h/e.sup.2, which is 25.8
k.OMEGA..
[0016] FIG. 8 is a graph showing dependences of R.sub.yx and
R.sub.xx on different back gate voltages (V.sub.b) of the
embodiment of FIG. 6, wherein units of R.sub.yx and R.sub.xx are
both quantum resistance (h/e.sup.2, i.e., 25.8 k.OMEGA.).
[0017] FIG. 9 is a graph showing a dependence of arctangent of Hall
angle
.alpha. = R yx R xx ##EQU00001##
on different back gate voltages (V.sub.b) of the embodiment of FIG.
6.
[0018] FIG. 10 is a graph showing magnetic field (.mu..sub.0H)
dependent Hall resistances (R.sub.yx) of another embodiment of
magnetically doped TI quantum well film at different back gate
voltages (V.sub.b), wherein the unit of R.sub.yx is k.OMEGA..
[0019] FIG. 11 is a graph showing magnetic field dependent
longitudinal resistances (R.sub.xx) of the embodiment of FIG. 10 at
different back gate voltages (V.sub.b), wherein the unit of
R.sub.xx is k.OMEGA..
[0020] FIG. 12 is a graph showing a dependence of Hall angle
.alpha. = R yx R xx ##EQU00002##
on different back gate voltages (V.sub.b) of the embodiment of FIG.
10.
[0021] FIG. 13 is a graph showing magnetic field (.mu..sub.0H)
dependent Hall resistances (R.sub.yx) of yet another embodiment of
magnetically doped TI quantum well film at different back gate
voltages (V.sub.b), wherein the unit of R.sub.yx is quantum
resistance (h/e.sup.2, i.e., 25.8 k.OMEGA.).
[0022] FIG. 14 is a graph showing magnetic field (.mu..sub.0H)
dependent longitudinal resistances (R.sub.xx) of the embodiment of
FIG. 13 at different back gate voltages (V.sub.b), wherein the unit
of R.sub.xx is quantum resistance (h/e.sup.2, i.e., 25.8
k.OMEGA.).
[0023] FIG. 15 is a graph showing a dependence of Hall angle
.alpha. = R yx R xx ##EQU00003##
on different back gate voltages (V.sub.b) of the embodiment of FIG.
13.
[0024] FIG. 16 is a graph showing magnetic field (.mu..sub.0H)
dependent Hall resistances (R.sub.yx) of a comparative sample (1)
at different back gate voltages (V.sub.b), wherein the unit of
R.sub.yx is .OMEGA..
[0025] FIG. 17 is a graph showing a dependence of longitudinal
resistance (R.sub.xx) on different back gate voltages (V.sub.b) of
the comparative sample (1) of FIG. 16, wherein the unit of R.sub.xx
is .OMEGA..
[0026] FIG. 18 is a graph showing dependences of R.sub.yx and
carrier density (n.sub.2D) on different back gate voltages
(V.sub.b) of the comparative sample (1) of FIG. 16, wherein the
unit of R.sub.yx is .OMEGA..
[0027] FIG. 19 is a graph showing magnetic field (.mu..sub.0H)
dependent Hall resistances (R.sub.yx) of a comparative sample (2)
at different back gate voltages (V.sub.b), wherein the unit of
R.sub.yx is .OMEGA..
[0028] FIG. 20 is a graph showing magnetic field (.mu..sub.0H)
dependent Hall resistances (R.sub.yx) of a comparative sample (3)
at different back gate voltages (V.sub.b), wherein the unit of
R.sub.yx is .OMEGA..
DETAILED DESCRIPTION
[0029] The disclosure is illustrated by way of example and not by
way of limitation in the figures of the accompanying drawings in
which like references indicate similar elements. It should be noted
that references to "an" or "one" embodiment in this disclosure are
not necessarily to the same embodiment, and such references mean at
least one.
[0030] An embodiment of a method for generating QAHE includes steps
of: [0031] S21, forming a TI quantum well film in a 3 QL thickness
to 5 QL thickness on the insulating substrate; [0032] S22, doping
the TI quantum well film with a first chemical element and a second
chemical element during the forming of the TI quantum well film to
form the magnetically doped TI quantum well film, the doping with
the first chemical element and the second chemical element
respectively introducing hole type charge carriers and electron
type charge carriers in the magnetically doped TI quantum well
film, to decrease the carrier density of the magnetically doped TI
quantum well film to be smaller than or equal to 1.times.10.sup.13
cm.sup.-2, one of the first element and the second element
magnetically doping the TI quantum well film (i.e., one of the
first element and the second element is the magnetically dopant to
the topological insulator quantum well film); [0033] S23, applying
an electric field to the magnetically doped TI quantum well film to
further decrease the carrier density to a degree at which the QAHE
is achieved.
[0034] The steps S21 and S22 are performed simultaneously. The
forming of the TI quantum well film is the doping of the TI quantum
well film to form the magnetically doped TI quantum well film.
[0035] A material of the undoped TI quantum well film can be
antimony telluride (Sb.sub.2Te.sub.3). A material of the
magnetically doped TI quantum well film can be Sb.sub.2Te.sub.3
doped by chromium (Cr) and bismuth (Bi) substituting some of the Sb
in the Sb.sub.2Te.sub.3, which can be represented by a chemical
formula Cr.sub.y(Bi.sub.xSb.sub.1-x).sub.2-yTe.sub.3, wherein
0<x<1, 0<y<2. The doping with Cr introduces hole type
charge carriers and the doping with Bi introduces electron type
charge carriers into the magnetically doped TI quantum well film.
The values of x and y satisfy that the amount of the hole type
charge carriers introduced by the Cr doping is substantially equal
to the amount of the electron type charge carriers introduced by
the Bi doping. By satisfying this, the carrier density of the
magnetically doped TI quantum well film is equal to or smaller than
1.times.10.sup.13 cm.sup.-2 without applying a voltage thereto
(i.e., at zero electric field). Thus, the effectiveness of a gate
voltage tuning method can be guaranteed during the realization of
the QAHE by the magnetically doped TI quantum well film. The
magnetically doped TI quantum well film has 3 QL to 5 QL, and has a
thickness in a range from 3 QL thickness to 5 QL thickness (about 3
nanometers to about 5 nanometers), wherein "QL" means "quintuple
layer". "QL thickness" means the thickness of the quintuple
layer.
[0036] The magnetically doped TI quantum well film is formed by
doping the Sb.sub.2Te.sub.3 with Cr atoms and Bi atoms to replace
some of the Sb atoms therein. Sb.sub.2Te.sub.3 is a layer-type
material, belonging to the trigonal crystal system, and has a space
group of D.sub.3d.sup.5(R 3m). Referring to FIG. 1, on the xy
plane, Sb atoms and Te atoms are respectively arranged in a
hexagonal close packing style to form Sb atom layers and Te atom
layers. Sb atom layers and Te atom layers are alternately laminated
along the direction z perpendicular to the xy plane. Each QL
consists of five adjacent atom layers. In
Cr.sub.y(Bi.sub.xSb.sub.1-x).sub.2-yTe.sub.3, the five adjacent
atom layers of one QL are the first Te atom layer (Te1), the Cr and
Bi doped first Sb atom layer (Sb1), the second Te atom layer (Te2),
the Cr and Bi doped second Sb atom layer (Sb1'), and the third Te
atom layer (Te1'). In a single QL, the Sb (or Cr, Bi) atoms and Te
atoms are joined by covalent-ionic bonds. Between adjacent QLs, the
Te1 and Te1' are combined by van der Waals force, thus forming
cleavage planes between adjacent QLs. In
Cr.sub.y(Bi.sub.xSb.sub.1-x).sub.2-yTe.sub.3, the values of x and y
satisfy that the amount of the hole type charge carriers introduced
by the doping with Cr is substantially equal to the amount of the
electron type charge carriers introduced by the doping with Bi. In
one embodiment, 0.05<x<0.3, 0<y<0.3, and
1:2<x:y<2:1 (e.g., 2:3.ltoreq.x:y.ltoreq.25:22).
[0037] The material of the insulating substrate is not limited, and
only needs to be capable of having the magnetically doped TI
quantum well film located, grown, and/or formed thereon by a
molecular beam epitaxy (MBE) method. In one embodiment, the
material of the insulating substrate can have a dielectric constant
greater than 5000 at a temperature equal to or smaller than 10
Kelvin (K), such as strontium titanate (STO). To achieve the QAHE,
a chemical potential of the magnetically doped TI quantum well film
is tuned by applying an external electric field or voltage to the
magnetically doped TI quantum well film which is called the gate
voltage tuning method. More specifically, the electric field or
voltage can be applied to the magnetically doped TI quantum well
film through a top gate and/or a back gate on the magnetically
doped TI quantum well film. The chemical potential of the
magnetically doped TI quantum well film can be tuned by the field
effect. To achieve the QAHE, the defects in the magnetically doped
TI quantum well film need to be as few as possible to decrease the
carrier density in the magnetically doped TI quantum well film.
However, the top gate is formed by forming a dielectric layer and a
metal electrode on a surface of the magnetically doped TI quantum
well film, which increases the possibility of destroying the
magnetically doped TI quantum well film or introducing defects into
the magnetically doped TI quantum well film. The insulating
substrate, having a relatively large dielectric constant at a
relatively low temperature, can have a relatively large
capacitance, though the thickness of the insulating substrate is
relatively large. Thus, the insulating substrate having the
relatively large dielectric constant can be directly used as the
dielectric layer at the relatively low temperature between the back
gate and the magnetically doped TI quantum well film. The
insulating substrate has a first surface and a second surface
opposite to the first surface. The magnetically doped TI quantum
well film can be formed on the first surface. The back gate is
formed by forming a metal electrode on the second surface of the
insulating substrate. The forming of the back gate does not contact
to the magnetically doped TI quantum well film, thus avoids of
introducing defects to the magnetically doped TI quantum well film.
When the material of the insulating substrate is STO, the
magnetically doped TI quantum well film can be grown on a (111)
surface, which is used as the first surface. The (111) surface is a
surface along a (111) crystallographic plane of the STO. The
thickness of the STO insulating substrate can be in a range from
about 0.1 millimeters to about 1 millimeter.
[0038] In the steps S21 and S22, the magnetically doped TI quantum
well film can be formed on the insulating substrate through a
molecular beam epitaxy (MBE) method. One embodiment for forming the
magnetically doped TI quantum well film includes following steps
of:
[0039] S11, providing the STO substrate having the (111) surface,
the STO substrate is disposed in a ultra-high vacuum environment in
an MEB reactor chamber;
[0040] S12, cleaning the surface of the STO substrate by
heat-treating the STO substrate in the MEB chamber;
[0041] S13, heating the STO substrate and forming Bi beam, Sb beam,
Cr beam, and Te beam in the MEB chamber in a controlled ratio
achieved by controlling flow rates of the Bi beam, Sb beam, Cr
beam, and Te beam; and
[0042] S14, forming the magnetically doped TI quantum well film on
the (111) surface of the STO substrate,
[0043] wherein the controlled ratio of the Bi beam, Sb beam, Cr
beam, and Te beam makes that in the magnetically doped TI quantum
well film, the amount of the hole type charge carriers introduced
by the doping with Cr is substantially equal to the amount of the
electron type charge carriers introduced by the doping with Bi.
[0044] In the step S11, the (111) surface of the STO substrate is
smooth at atomic level. In one embodiment, the (111) surface of the
STO substrate is formed by steps of: cutting the STO substrate
along the (111) crystallographic plane; heating the STO substrate
in deionized water below 100.degree. C. (e.g., 70.degree. C.); and
burning the STO substrate in an environment of a combination of
O.sub.2 and Ar at a temperature in a range from about 800.degree.
C. to about 1200.degree. C. (e.g., 1000.degree. C.). A time period
for the heating in the deionized water can be in a range from about
1 hour to about 2 hours. A time period for the burning in the
environment of the combination of O.sub.2 and Ar can be in a range
from about 2 hours to about 3 hours.
[0045] MEB is a film evaporation-deposition method performed in
ultra-high vacuum (in a range from 1.0.times.10.sup.-11 mbar to
1.0.times.10.sup.-9 mbar, e.g., about 1.0.times.10.sup.-10 mbar) at
a deposition rate in a range from about 0.1 nm/s to about 1 nm/s to
evaporate a source and deposit the film at a low speed which allows
films to grow epitaxially. The absence of carry gases as well as
the ultra high vacuum environment results in the highest achievable
purity of grown films. The MBE reactor chamber can be joined with a
variable temperature scanning tunneling microscope (VTSTM) and
angle resolved photoemission spectroscopy (ARPES) to form a system.
The system can have in-situ VTSTM and ARPES tests of the
magnetically doped TI quantum well film.
[0046] During the forming of the magnetically doped TI quantum well
film and the VTSTM and ARPES tests of the magnetically doped TI
quantum well film, the magnetically doped TI quantum well film is
kept in the MBE reactor chamber having a degree of vacuum smaller
than 1.0.times.10.sup.-10 mbar (a pressure is less than
1.0.times.10.sup.-8 Pa). In this degree of vacuum, the density of
the gas molecules at room temperature is about
2.4.times.10.sup.6/cm.sup.3, and the average distance between the
gas molecules is about 0.1 millimeters. In this ultra-high vacuum
environment, the magnetically doped TI quantum well film having
high purity and few defects can be formed using the MBE method.
Meanwhile, in this ultra-high vacuum environment, the (111) surface
of the magnetically doped TI quantum well film can be kept clean
for a long time. In one embodiment, the MBE reactor chamber has a
degree of vacuum less than or equal to 5.0.times.10.sup.-1.degree.
mbar.
[0047] In the step S12, the temperature and time of the
heat-treating are selected to make the (111) surface of the STO
substrate as clean as possible. In one embodiment, the temperature
of the heat-treating is about 600.degree. C., and the time of the
heat-treating is about 1 hour to about 2 hours. The heat-treating
can remove organic substances, gas, and water adsorbed on the (111)
surface of the STO substrate.
[0048] In the step S13, the beams of Bi, Sb, Cr, and Te can be
generated by heating evaporating sources of Bi, Sb, Cr and Te. FIG.
2 shows that in the reactor chamber, four independent evaporating
sources can be arranged by respectively disposing solid Bi, Sb, Cr,
and Te in four Knudsen cells (K-Cell). One Knudsen cell is composed
of a crucible, a heating filament, a water cooling system, an
orifice shutter, and a thermocouple. A material of the crucible can
be pyrolytic boron nitride or Al.sub.2O.sub.3. The solid Bi, Sb,
Cr, and Te are respectively disposed in the crucibles. All the
solid Bi, Sb, Cr, and Te have the purity larger than or equal to 5N
degree (99.999%). The heating filaments (e.g., tantalum filaments
or tungsten filaments) are used to heat the crucibles to evaporate
the solid Bi, Sb, Cr, and Te, and the evaporating rate is
controlled by controlling the heating temperature. The orifice
shutter is used to cover the crucible to control the beginning and
ending of the evaporation. Thus, the uniformity of the ratio among
the Bi, Sb, Cr, and Te in the formed magnetically doped TI quantum
well film can be controlled. The water cooling system is used to
decrease the temperature around the evaporating source, thus keeps
a relatively good vacuum and decreases the impurity in the MBE
reactor chamber. The STO substrate is disposed in the MEB reactor
chamber and spaced from the evaporating sources. The (111) surface
of the STO substrate faces to the evaporating sources. A heater can
be further located on a back side (e.g., near the second surface)
of the STO substrate opposite to the (111) surface to heat the STO
substrate.
[0049] The flow rate can be a mass flow rate or a volumetric flow
rate, which is a mass or a volume of a fluid passing through a
given surface per unit of time. The flow rates of Bi, Sb, Cr, and
Te are represented as V.sub.Bi, V.sub.Sb, V.sub.Cr, and V.sub.Te
respectively, and satisfy V.sub.Te>(V.sub.Cr+V.sub.Bi+V.sub.Sb),
to ensure that the magnetically doped TI quantum well film is
formed in a Te environment, to decrease the amount of Te vacancies
in the magnetically doped TI quantum well film. In one embodiment,
(V.sub.Cr+V.sub.Bi+V.sub.Sb):V.sub.Te is in a range from about 1:10
to about 1:15. However, the V.sub.Te cannot be too large. A
relatively large V.sub.Te tends to induce an aggregation of the Te
atoms on the (111) surface of the STO substrate. The V.sub.Bi,
V.sub.Sb, V.sub.Cr, and V.sub.Te can be controlled by controlling
the temperatures of the four evaporating sources, and can be
measured by a flow meter (e.g., quartz oscillation type gas flow
meter).
[0050] In step S14, during the forming of the magnetically doped TI
quantum well film, the STO substrate may need to be heated to a
proper temperature (e.g., in a range from about 180.degree. C. to
about 250.degree. C.). The temperature of the heating of the STO
substrate can ensure the decomposition of Te.sub.2 and/or Te.sub.4
molecule into Te atoms, while ensuring the formation of a single
crystal magnetically doped TI quantum well film. An approximate
value of the ratio among the Bi, Sb, Cr, and Te in the magnetically
doped TI quantum well film can be estimated by the flow meter, and
an accurate value can be achieved by chemical element analysis of a
thick sample (e.g., having a thickness of 100 QL) formed by the
same method. In one embodiment, the heating temperature of the
substrate (T.sub.sub) is about 180.degree. C. to about 200.degree.
C., the evaporating temperature of Te source (T.sub.Te) is about
310.degree. C., the evaporating temperature of Bi source (T.sub.Bi)
is about 500.degree. C., the evaporating temperature of Sb source
(T.sub.Sb) is about 360.degree. C., and the evaporating temperature
of Cr source (T.sub.Cr) is about 1020.degree. C. The STO substrate
can be heated by tungsten filaments disposed on the back side of
the STO substrate. In one embodiment, when the magnetically doped
TI quantum well film is a 5 QL film, the first QL of the
magnetically doped TI quantum well film is formed at a lower
heating temperature of the STO substrate (e.g.,
T.sub.sub=180.degree. C.), and the other 4 QL are formed on the
first QL at a higher heating temperature (e.g.,
T.sub.sub=200.degree. C.). A high temperature of the STO substrate
may cause the surface of the first QL to be uneven. These two
temperature periods can ensure that the first QL uniformly and flat
on the substrate at a lower temperature, and the other 4 QL can
have a high quality at the higher temperature.
[0051] After step S14, a step of annealing the magnetically doped
TI quantum well film can be processed to further decrease the
defects in the magnetically doped TI quantum well film. The
magnetically doped TI quantum well film can be heated at an
annealing temperature for an annealing time. In one embodiment, the
annealing temperature can be in a range from about 180.degree. C.
to about 250.degree. C. (e.g., 200.degree. C.), an annealing time
can be in a range from about 10 minutes to about 1 hour (e.g., 20
minutes).
[0052] Formation of the magnetically doped TI quantum well film is
not limited to the above described method. In another embodiment,
the material of the insulating substrate can be Al.sub.2O.sub.3,
and the insulating substrate can be a single crystal sapphire
substrate. However, because the dielectric constant of sapphire is
only about 20 at a low temperature, the sapphire substrate cannot
be used as the dielectric layer for the back gate. Thus, the top
gate structure may be used to tune the chemical potential of the
magnetically doped TI quantum well film. More specifically, a solid
dielectric layer (e.g., Al.sub.2O.sub.3 film, HfO.sub.2 film, or
MgO film) having a small thickness (e.g., 300 nanometers) can be
formed on the surface of the magnetically doped TI quantum well
film, and a metal electrode as the top gate can then be formed on
the surface of the dielectric layer.
[0053] In another embodiment, to avoid damaging or negatively
affecting the structure of the magnetically doped TI quantum well
film, a liquid top gate structure can be used to tune the chemical
potential. More specifically, a liquid dielectric layer can be
formed by dropping a drop of ionic liquid on the surface of the
magnetically doped TI quantum well film, and a metal electrode as
the top gate can be arranged to be in contact with the liquid
dielectric layer but spaced from the magnetically doped TI quantum
well film.
[0054] In step S23, when the insulating substrate has a relatively
large dielectric constant, the electric field can be applied only
by the back gate structure. The electric field can be in a range of
.+-.200V. Step S23 can be processed at a low temperature (e.g.,
smaller than or equal to 10 Kelvin (K)). In one embodiment, the
step S23 is processed at a temperature smaller than or equal to 1.5
K.
[0055] As mentioned in the background, Sb.sub.2Te.sub.3 TI film
makes it possible to realize the QAHE. Theoretically, Cr can
equivalently substitute Sb of the Sb.sub.2Te.sub.3 to achieve the
Cr doped Sb.sub.2Te.sub.3. The QAHE can be achieved by doping the
Sb.sub.2Te.sub.3 TI film with Cr having an infinite uniformity to
achieve the ferromagnetism of the TI film. This ferromagnetism
achieved by the doping is different from RKKY type ferromagnetism
in traditional diluted magnetic semiconductors and does not need
charge carriers, thus keeping the system in the insulating
state.
[0056] However, the inventors found that in a real system, the
carrier density in the Cr doped Sb.sub.2Te.sub.3 is very large. The
carrier density can be calculated by n.sub.2D=1/eR.sub.H, wherein
R.sub.H is a slope (or gradient) of a Hall curve (i.e., a curve of
magnetic field to Hall resistance). The tested carrier density of
the Sb.sub.2Te.sub.3 quantum well film with Cr doped on Sb sites
has a carrier density in a scale of 10.sup.14 cm.sup.-2. It is
impossible to tune that large of a carrier density by using either
back gate structure or top gate structure. That large of a carrier
density is mainly caused by the defects introduced during the Cr
doping of the Sb.sub.2Te.sub.3. Numerous factors such as forming
conditions and environment conditions affect the forming of the
film. It is extremely difficult to dope the Sb.sub.2Te.sub.3 with
Cr to the infinite degree of uniformity. During the Cr doping, the
defects are introduced into the Sb.sub.2Te.sub.3 quantum well film.
FIG. 3 shows that an image of Cr doped Sb.sub.2Te.sub.3 at atomic
resolution achieved by VTSTM, the triangle shaped defects are the
locations of Cr dopants. Theoretically, the substitution of Sb
atoms with Cr atoms does not introduce extra charge carriers.
However, in a real system, the doping cannot be infinitely uniform.
Non-bonded Cr atoms can exist in the film and introduce extra
charge carriers, which is the hole type charge carriers tested by
inventors. The carrier density is too large to be decreased to a
level to realize the QAHE.
[0057] In the present disclosure, to solve the problem that the
magnetic dopant (e.g., Cr) may introduce defects, another dopant
(e.g., Bi) which can introduce the adverse type of defects is used
with the magnetic dopant, and the gate voltage tuning method is
also used. Thus, the QAHE can be realized. For example,
Sb.sub.2Te.sub.3 is doped by both Cr and Bi to form a quaternary
system in the film. The doping of Sb.sub.2Te.sub.3 with Cr and Bi
can simultaneously introduce two adverse types of defects. The
defects (hole type) introduced by Cr can be substantially
neutralized by the defects (electron type) introduced by another
kind of dopant (e.g., Bi), thus decreasing the carrier density in
the material. Thus, the quaternary system can have the
ferromagnetic property while having a low level of carrier density.
The amount of Bi doped in the Sb.sub.2Te.sub.3 (i.e., the value of
x in Cr.sub.y(Bi.sub.xSb.sub.1-x).sub.2-yTe.sub.3) depends on the
amount of defects introduced by Cr. The amount of defects
introduced by Cr may be affected by factors such as forming
conditions and environmental conditions. The amount of defects
introduced by Cr can be analyzed previously by forming a
Cr.sub.ySb.sub.2-yTe.sub.3 film under the same conditions. In one
embodiment, 0.05<x<0.3, 0<y<0.2, and 1:2<x:y<2:1
(e.g., 2:3.ltoreq.x:y.ltoreq.25:22). By adjusting the amount of Bi
and Cr (i.e., adjusting the values of x and y), the amount of the
hole type charge carriers introduced by the doping with Cr is
substantially equal to the amount of the electron type charge
carriers introduced by the doping with Bi, and the carrier density
in the magnetically doped TI quantum well film can be decreased to
a level that is capable of being tuned by the gate tuning method.
By using the gate tuning method to tune the quaternary system, the
magnetically doped TI quantum well film can have the carrier
density near zero, and have the anomalous Hall resistance
(R.sub.AH) in a range of 0.3.times.25.8
k.OMEGA..ltoreq.R.sub.AR.ltoreq.1.times.25.8 k.OMEGA. (i.e., 7.74
k.OMEGA..ltoreq.R.sub.AR.ltoreq.25.8 k.OMEGA.), while the anomalous
Hall angle is (.alpha.=R.sub.AH/R.sub.xx).gtoreq.0.2.
[0058] An embodiment of an electrical device based on the
magnetically doped TI quantum well film is provided. The electrical
device includes the above described magnetically doped TI quantum
well film. The electrical device includes an insulating substrate
including a first surface and a second surface opposite to the
first surface, and the magnetically doped TI quantum well film
grown on the first surface of the insulating substrate. A material
of the magnetically doped TI quantum well film is represented by a
chemical formula of Cr.sub.y(Bi.sub.xSb.sub.1-xi).sub.2-yTe.sub.3,
wherein 0<x<1, 0<y<2. The doping with Cr introduces
hole type charge carriers and the doping with Bi introduces
electron type charge carriers into the magnetically doped TI
quantum well film. The values of x and y satisfy that the amount of
the hole type charge carriers introduced by the doping with Cr is
substantially equal to the amount of the electron type charge
carriers introduced by the doping with Bi. The thickness of the
magnetically doped TI quantum well film is in a range from 3 QL to
5 QL. The anomalous Hall resistance (R.sub.AH) of the magnetically
doped TI quantum well film is in a range of 0.3.times.25.8
k.OMEGA..ltoreq.R.sub.AR.ltoreq.1.times.25.8 k.OMEGA. (i.e., 7.74
k.OMEGA..ltoreq.R.sub.AR.ltoreq.25.8 k.OMEGA.), while the anomalous
Hall angle is (.alpha.=R.sub.AH/R.sub.xx).gtoreq.0.2.
[0059] In one embodiment, the electrical device further includes a
back gate electrode and two conducting electrodes (i.e., source
electrode and drain electrode). The back gate electrode is used to
tune the chemical potential of the magnetically doped TI quantum
well film. The two conducting electrodes are used to conduct an
electrical current through the magnetically doped TI quantum well
film along a first direction.
[0060] In one embodiment, the electrical device can further include
three output electrodes (e.g., E1, E2 and E3), which are used to
test the resistances of the magnetically doped TI quantum well film
in the first direction (i.e., the longitudinal resistance) and in
the second direction (i.e., the Hall resistance).
[0061] All the above mentioned electrodes can be formed by using an
E-beam method. The material of the electrodes can be selected
according to having good conductivity (e.g., gold or titanium). In
another embodiment, the electrodes can be formed by coating an
indium paste or silver paste on the surface of the magnetically
doped TI quantum well film.
[0062] More specifically, the back gate electrode is located on the
second surface of the insulating substrate. The two conducting
electrodes and three output electrodes are arranged on the top
surface of the magnetically doped TI quantum well film and spaced
from each other. The two conducting electrodes and three output
electrodes are electrically connected to the magnetically doped TI
quantum well film. The two conducting electrodes are arranged at
two opposite sides of the magnetically doped TI quantum well film.
A line extending from one conducting electrode to the other
conducting electrode is the first direction. A line extending from
E1 to E2 is the first direction, and a line extending from E2 to E3
is the second direction. The first direction is perpendicular to
the second direction. The E1, E2 and E3 can be arranged at two
opposite sides in the second direction of the magnetically doped TI
quantum well film. For example, E1 and E2 can be arranged to the
same side, and E3 can be arranged on the other side. The two
conducting electrodes can be bar shaped with a relatively long
length approximately equal to the length of the magnetically doped
TI quantum well film in the second direction. The length direction
of the conducting electrodes can be parallel to the second
direction. The three output electrodes can be spot electrodes.
[0063] Referring to FIG. 4 and FIG. 5, in the figure, x represents
the first direction and y represents the second direction. In one
embodiment of the electrical device 10, the magnetically doped TI
quantum well film 20 formed on the first surface of the insulating
substrate 30 has a shape including a rectangular central part 22,
two first connecting parts 24 extended from the central part 22 to
the two conducting electrodes 50, and three second connecting parts
26 extended from the central part 22 to the E1, E2, and E3. The
three second connecting parts 26 are spaced from each other. The
length of the central part 22 in the second direction is smaller
than the length of the conducting electrode 50.
[0064] The first connecting parts 24 can have a trapezoid shape
having two parallel sides parallel to the second direction, the
longer one is joined to the conducting electrode 50, the shorter
one is joined to the central part 22. The three second connecting
parts 26 can extend along the second direction. In one embodiment,
the three second connecting parts 26 can extend from three corners
of the rectangle central part 22 to E1, E2, and E3. The back gate
electrode 40 is located on the second surface of the insulating
substrate 30.
[0065] The conducting electrode 50 can be located on a top surface
of the first connecting parts 24 at a side. The pattern of the
magnetically doped TI quantum well film 20 having the narrow
rectangular central part 22 and the trapezoid shaped first
connecting parts 24 connected to the long conducting electrode 50
can decrease the contacting resistance. The second connecting part
26 can have a strip shape with a narrow width. The output electrode
is located on a top surface of the second connecting part 26 at one
end. The other end of the second connecting part 26 is joined to
the central part 22.
[0066] The rectangular central part 22 can have a length of about
100 microns to about 400 microns (e.g., 200 microns) in the first
direction, and a length of about 10 microns to about 40 microns
(e.g., 20 microns) in the second direction.
[0067] The conducting electrode 50 can have a length of about 1
millimeter to about 4 millimeters (e.g., 2 millimeters) in the
second direction, and a length of about 5 millimeters to about 10
millimeters in the first direction.
[0068] In addition, the electrical device can further include a
fourth output electrode E4 similar to E1, E2, and E3. E4 is spaced
from E1, E2, and E3, and located on a surface of the magnetically
doped TI quantum well film 20. A direction from E3 to E4 is the
first direction, and a direction from the E1 to E4 is the second
direction. Correspondingly, the magnetically doped TI quantum well
film 20 can includes four second connecting parts 26 respectively
extended from the central part 22 to E1, E2, E3, and E4 from the
four corners of the central part 22.
[0069] The pattern of the magnetically doped TI quantum well film
20 can formed by removing other portion of the magnetically doped
TI quantum well film 20 by mechanical scraping method, ultraviolet
lithography method, or electron beam lithography method.
Experiments on Some Embodiments
[0070] Different embodiments of the electrical devices are formed
by using different magnetically doped TI quantum well films. During
an experiment of an electrical device, constant electric current is
conducted through the magnetically doped TI quantum well film by
the two conducting electrodes at a low temperature. Resistances
R.sub.xx and R.sub.yx in different directions of the magnetically
doped TI quantum well film are measured by using the three output
electrodes, wherein R.sub.xx is the resistance along the direction
of the constant electric current (i.e., the first direction), and
R.sub.yx is the resistance along the direction perpendicular to the
constant electric current (i.e., the second direction). The
R.sub.yx is the Hall resistance. Top gate structure or back gate
structure may be used to tune the chemical potential of the
magnetically doped TI quantum well film in the experiment. The top
gate voltage is represented by V.sub.t, and the back gate voltage
is represented by V.sub.b.
[0071] The magnetic property of the magnetically doped TI quantum
well film is studied by a superconducting quantum interference
device (SQUID).
[0072] In the magnetic materials, R.sub.yx=R.sub.AM(T,H)+R.sub.NH,
wherein R.sub.A is the anomalous Hall coefficient, M(T,H) is the
magnetization, R.sub.N is the normal Hall coefficient. H is an
external magnetic field. The value of the anomalous Hall resistance
is defined as the value of the Hall resistance (R.sub.yx) at zero
magnetic field. The R.sub.AM(T,H) is the anomalous Hall resistance
(R.sub.AH=R.sub.AM(T,H)), which is related to the magnetization
(i.e., M(T,H)), and plays the major part of R.sub.yx at a low
magnetic field. The R.sub.NH is the normal Hall resistance, which
is the linear part of R.sub.yx at a high magnetic field. R.sub.N
decides the carrier density (n.sub.2D), and the type of the charge
carriers. The following experiments are processed at near zero
magnetic field (i.e., H=0). Thus, the R.sub.yx can be seen as equal
to the R.sub.AH.
Embodiment 1 (T=30 mK, 5QL Sample, Back Gate Structure)
[0073] The magnetically doped TI quantum well film is 5QL
Cr.sub.0.15(Bi.sub.0.10Sb.sub.0.9).sub.1.85Te.sub.3 (i.e., the film
has 5 QL), and the substrate 30 is STO substrate, in the embodiment
1. Different back gate voltages (Vb) are applied to the
magnetically doped TI quantum well film, and the corresponded Hall
curves are tested at the temperature of 30 mK.
[0074] Referring to FIGS. 6 to 9, H is the magnetization and
.mu..sub.0 is the vacuum permeability, in the .mu..sub.0H. The unit
of .mu..sub.0H is Tesla (T). The R.sub.AH of the sample is changed
with V.sub.b, and the hysteresis phenomena can be seen, which means
that the sample has a good ferromagnetic property. When
0V.ltoreq.V.sub.b.ltoreq.10V, the change of R.sub.AH with V.sub.b
is not very great. When V.sub.b=-4.5 V, R.sub.AH=25.8 k.OMEGA.. The
QAHE is realized.
Embodiment 2 (T=1.5K, 4QL Sample, Back Gate Structure)
[0075] The magnetically doped TI quantum well film is 4QL
Cr.sub.0.22(Bi.sub.0.22Sb.sub.0.78).sub.1.78Te.sub.3, and the
substrate 30 is STO substrate, in the embodiment 2.
[0076] Different back gate voltages (V.sub.b) are applied to the
magnetically doped TI quantum well film, and the corresponded Hall
curves are tested at the temperature of 1.5K. Referring to FIG. 10,
the hysteresis phenomena can be seen, and the hysteresis loops have
a "square" shape, which means that the sample has a great
ferromagnetic property. By changing V.sub.b, a relatively large
R.sub.AH can be achieved. The R.sub.AH increases first and then
decreases with the increasing of the V.sub.b. When V.sub.b=45 V,
R.sub.AH reaches the maximum value, which is 10 k.OMEGA.. This
value is approximate to 0.4 quantum resistance, the quantum
resistance is 25.8 k.OMEGA.. FIG. 11 shows that the
R.sub.xx-.mu..sub.0H curves show a butterfly shaped hysteresis
pattern, which also reveals that the sample has a great
ferromagnetic property. In addition, when V.sub.b=45V, the
anomalous Hall angle (.alpha.=R.sub.AH/R.sub.xx) is as high as
0.42, which is twice of that value of the 5QL sample. FIG. 12 shows
that the Hall angle (R.sub.yx/R.sub.xx) increases first and then
decreases with the increasing of the V.sub.b.
Embodiment 3 (T=100 mK, 4QL Sample, Back Gate Structure)
[0077] The magnetically doped TI quantum well film is 4QL
Cr.sub.0.22(Bi.sub.0.22Sb.sub.0.78).sub.1.78Te.sub.3, and the
substrate 30 is STO substrate, in the embodiment 3.
[0078] Different back gate voltages (V.sub.b) are applied to the
magnetically doped TI quantum well film, and the corresponded Hall
curves are tested at the temperature of 100 mK. FIG. 13 shows that
the hysteresis phenomena can be seen, which means that the sample
has a good ferromagnetic property. When
0V.ltoreq.V.sub.b.ltoreq.20V, the change of R.sub.AH with V.sub.b
is not very great. R.sub.AH is about 0.6 quantum resistance. When
V.sub.b=10 V, R.sub.AH reaches the maximum value,
(R.sub.AH).sub.max=0.59he.sup.-2, which is about 15.3 k.OMEGA..
This value exceeds a half of quantum resistance and is larger than
the greatest known anomalous Hall resistance ever achieved in the
world at this time. FIG. 14 shows that the change of the R.sub.xx
with the change of the V.sub.b is more obviously than the change of
the R.sub.yx with the change of V.sub.b as shown in FIG. 13.
Especially, when V.sub.b=0V, the anomalous Hall angle
(.alpha.=R.sub.AH/R.sub.xx)>0.5. FIG. 15 shows that the Hall
angle (R.sub.yx/R.sub.xx) increases first and then decreases with
the increasing of the V.sub.b.
Embodiment 4 (T=90 mK, 5QL Sample, Back Gate Structure,
V.sub.t=0)
[0079] The magnetically doped TI quantum well film is 5QL
Cr.sub.0.15(Bi.sub.0.1Sb.sub.0.9).sub.1.85Te.sub.3, and the
substrate 30 is STO substrate having a thickness of 0.25
millimeters, in the embodiment 4. Different back gate voltages
(V.sub.b) are applied to the magnetically doped TI quantum well
film at the temperature of 90 mK. When V.sub.b=30 V, the maximum
R.sub.AH is about 24.1 k.OMEGA..
Embodiment 5 (T=400 mK, 5QL Sample, Back Gate Structure,
V.sub.t=0)
[0080] The magnetically doped TI quantum well film is 5QL
Cr.sub.0.15(Bi.sub.0.1Sb.sub.0.9).sub.1.85Te.sub.3, and the
substrate 30 is STO substrate having a thickness of 0.25
millimeters, in the embodiment 5. Different back gate voltages
(V.sub.b) are applied to the magnetically doped TI quantum well
film at the temperature of 400 mK. When V.sub.b=20 V, the maximum
R.sub.AH is about 23.0 k.OMEGA..
Embodiment 6 (T=1.5 K, 5QL Sample, Back Gate Structure,
V.sub.t=0)
[0081] The magnetically doped TI quantum well film is 5QL
Cr.sub.0.15(Bi.sub.0.1Sb.sub.0.9).sub.1.85Te.sub.3, and the
substrate 30 is STO substrate having a thickness of 0.25
millimeters, in the embodiment 6. Different back gate voltages
(V.sub.b) are applied to the magnetically doped TI quantum well
film at the temperature of 1.5 K. When V.sub.b=28 V, the maximum
R.sub.AH is about 19.02 k.OMEGA..
[0082] The experiment results of the embodiments 1 to 6 are shown
in the Table 1.
TABLE-US-00001 TABLE 1 Hall V.sub.b R.sub.AH resistivity,
.rho..sub.yx R.sub.xx No. Sample Thickness Temperature (V)
(k.OMEGA.) (.mu..OMEGA. m) (k.OMEGA.) R.sub.AH/R.sub.xx 1
Cr.sub.0.15(Bi.sub.0.10Sb.sub.0.9).sub.1.85Te.sub.3 5QL 30 mK -4.5
25.8 127.3 3.4 7.58 2
Cr.sub.0.22(Bi.sub.0.22Sb.sub.0.78).sub.1.78Te.sub.3 4QL 1.5 K 45
10 50 23.8 0.42 3
Cr.sub.0.22(Bi.sub.0.22Sb.sub.0.78).sub.1.78Te.sub.3 4QL 100 mK 10
15.3 76.5 34 0.45 4
Cr.sub.0.15(Bi.sub.0.1Sb.sub.0.9).sub.1.85Te.sub.3 5QL 90 mK 30
24.1k 120 7 3.44 5
Cr.sub.0.15(Bi.sub.0.10Sb.sub.0.9).sub.1.85Te.sub.3 5QL 400 mK 20
23.0 115 13 1.7 6
Cr.sub.0.15(Bi.sub.0.10Sb.sub.0.9).sub.1.85Te.sub.3 5QL 1.5 K 28
19.02 95.1 18.88 1.0007
COMPARATIVE EXAMPLES
[0083] (1) Sb.sub.2-yCr.sub.yTe.sub.3
[0084] By changing the doping amount of Cr, the material of Cr
doped Sb.sub.2Te.sub.3 TI quantum well film can be represented as
Sb.sub.2-yCr.sub.yTe.sub.3. Four samples of 5QL
Sb.sub.2-yCr.sub.yTe.sub.3 TI quantum well films are formed on the
(111) surface of the STO substrate, wherein y is 0, 0.05, 0.09, and
0.14 respectively. The experiment results reveal that when y=0,
Sb.sub.2-yCr.sub.yTe.sub.3 is Sb.sub.2Te.sub.3, and 5QL
Sb.sub.2Te.sub.3 has a linear dispersion surface state, the Dirac
point is located above the Fermi level (E.sub.F) and at 65 meV.
When doping Cr to the Sb.sub.2Te.sub.3, the location of the Dirac
point moves from +75 meV when y=0.05 to +88 meV when y=0.14. The
E.sub.F of all the four samples is not at a magnetically induced
gap-opening.
[0085] Without Bi doping, the 5QL Sb.sub.1.91Cr.sub.0.09Te.sub.3 TI
quantum well films are tuned by using the back gate structure. FIG.
16 and FIG. 17 show that R.sub.xx always increases with the
increasing of V.sub.b, which is a typical hole type semiconductor
behavior. Thus, it can be known that the tuning has no affection to
the type of carriers. The carrier type does not change during the
tuning step. During the tuning step, the mobility (.mu.) does not
change, and bases on the equation
R.sub.xx.sup.-1xx=.sigma..sub.xx=.mu.n.sub.2De, it shows that
n.sub.2D decreases with the increasing of V.sub.b in FIG. 18. FIG.
16 is the Hall curves of the 5QL Sb.sub.1.91Cr.sub.0.09Te.sub.3 at
different V.sub.b when T=1.5 K. The voltage range of the V.sub.b is
from about -210 V to about +210 V. The anomalous Hall resistance
(R.sub.AH) always increases with the increasing of V.sub.b. When
V.sub.b=-210 V, R.sub.AH=24.1.OMEGA., and
n.sub.2D=3.4.times.10.sup.14 cm.sup.-2. When V.sub.b=+210V,
R.sub.AH=40.8.OMEGA., and n.sub.2D=9.7.times.10.sup.13cm.sup.-2.
The relations between R.sub.AH and n.sub.2D to V.sub.b are shown in
FIG. 18. It can be seen from the FIG. 18 that R.sub.AH increases
with the decreasing of n.sub.2D. This phenomenon is completely
different from the traditional diluted magnetic semiconductors. In
the diluted magnetic semiconductor, the larger the n.sub.2D, the
larger the R.sub.AH. However, the R.sub.AH is still to low to
achieve QAHE.
[0086] (2) Bi.sub.1.78Cr.sub.0.22Se.sub.3
[0087] By changing the doping amount of Cr, the material of Cr
doped Bi.sub.2Se.sub.3 TI quantum well film can be represented as
Bi.sub.2-yCr.sub.ySe.sub.3. By selecting y=0.22, the thickness is
10 QL thickness, a sample of 10 QL Bi.sub.1.78Cr.sub.0.22Se.sub.3
TI quantum well film is formed. Referring to FIG. 19, when T=1.5K,
there is no hysteresis loop observed in the Hall effect experiment,
which indicates that Cr doped Bi.sub.2Se.sub.3 is a paramagnetic
material. Therefore, the Cr doped Bi.sub.2Se.sub.3 cannot have the
QAHE.
[0088] (3) Bi.sub.1.78Cr.sub.0.22Te.sub.3
[0089] By changing the doping amount of Cr, the material of Cr
doped Bi.sub.2Te.sub.3 TI quantum well film can be represented as
Bi.sub.2-yCr.sub.yTe.sub.3. By selecting y=0.22, the thickness is
10 QL thickness, a sample of 10 QL Bi.sub.1.78Cr.sub.0.22Te.sub.3
TI quantum well film is formed. FIG. 20 shows that when T=25K,
there is hysteresis loops observed in the Hall effect experiment,
which indicates that Cr doped Bi.sub.2Se.sub.3 is a ferromagnetism
material.
[0090] It is to be understood that the above-described embodiment
is intended to illustrate rather than limit the disclosure.
Variations may be made to the embodiment without departing from the
spirit of the disclosure as claimed. The above-described
embodiments are intended to illustrate the scope of the disclosure
and not restricted to the scope of the disclosure.
[0091] It is also to be understood that the above description and
the claims drawn to a method may include some indication in
reference to certain steps. However, the indication used is only to
be viewed for identification purposes and not as a suggestion as to
an order for the steps.
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